US8731258B2  Method and apparatus for efficient threedimensional contouring of medical images  Google Patents
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 US8731258B2 US8731258B2 US13295494 US201113295494A US8731258B2 US 8731258 B2 US8731258 B2 US 8731258B2 US 13295494 US13295494 US 13295494 US 201113295494 A US201113295494 A US 201113295494A US 8731258 B2 US8731258 B2 US 8731258B2
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 G06T2207/20092—Interactive image processing based on input by user
 G06T2207/20108—Interactive selection of 2D slice in a 3D data set

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 Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSSSECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSSREFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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 Y10S128/922—Computer assisted medical diagnostics including image analysis
Abstract
Description
This application is a continuation of U.S. patent application Ser. No. 11/848,624 filed Aug. 31, 2007, published as U.S. Pat. App. Pub. 2009/0060299, now U.S. Pat. No. 8,098,909, the entire disclosure of which is incorporated herein by reference.
This application is also related to U.S. patent application Ser. No. 13/295,525 filed this same day, which is a divisional U.S. patent application Ser. No. 11/848,624 filed Aug. 31, 2007, published as U.S. Pat. App. Pub. 2009/0060299, now U.S. Pat. No. 8,098,909.
The present invention pertains generally to the field of processing medical images, particularly generating contours for threedimensional (3D) medical imagery.
Contouring is an important part of radiation therapy planning (RTP), wherein treatment plans are customdesigned for each patient's anatomy. Contours are often obtained in response to user input, wherein a user traces the object boundary on the image using a computer workstation's mouse and screen cursor. However, it should also be noted that contours can also be obtained via automated processes such as autothresholding programs and/or autosegmentation programs.
Returning to the example of
Current RTP software typically limits contour drawing by the user through GUI 100 to T views (views which are perpendicular to the patient's long axis) as the T images usually have the highest spatial resolution, the T images are the standard representation of anatomy in the medical literature, and the T contours are presently the only format defined in the DICOM standard. The two other canonical views—the S and C views—can then be reconstructed from the columns and rows, respectively, of the T images.
When generating 3D surfaces from image slices, conventional software programs known to the inventor herein allow the user to define multiple T contours for a region of interest within an image for a plurality of different T image slices. Thereafter, the software program is used to linearly interpolate through the different T contours to generate a 3D surface for the region of interest. However, the inventor herein notes that it is often the case that a plane other than a T plane (e.g., planes within the S and/or C viewing planes) will often more clearly depict the region of interest than does the T plane. Therefore, the inventor herein believes there is a need in the art for a robust 3D contouring algorithm that allows the user to define input contours in any viewing plane (including S and C viewing planes) to generate a 3D surface for a region of interest and/or generate a new contour for the region of interest.
Further still, the inventor herein believes that conventional 3D surface generation techniques, particularly techniques for generating variational implicit surfaces, require unacceptably long computational times. As such, the inventor herein believes that a need exists in the art for a more efficient method to operate on contours in three dimensions.
Toward these ends, according to one aspect of an embodiment of the invention, disclosed herein is a contouring technique that increases the efficiency of 3D contouring operations by reducing the number of data points needed to represent a contour prior to feeding those data points to a 3D contouring algorithm, wherein the 3D contouring algorithm operates to generate a 3D surface such as a variational implicit surface or process the reduced data points to generate a new contour in a new plane via an interpolation technique such as Bspline interpolation. The data points that are retained for further processing are preferably a plurality of shapesalient points for the contour. In accordance with one embodiment, computed curvature values for the data points are used as the criteria by which to judge which points are shapesalient. In accordance with another embodiment, computed scalar second derivative values are used as the criteria by which to judge which points are shapesalient. In accordance with yet another embodiment, the DeBoor equal energy theorem is used as the criteria by which to judge which points are shapesalient.
According to another aspect of an embodiment of the invention, disclosed herein is a contouring technique that operates on a plurality of data points, wherein the data points define a plurality of contours corresponding to a region of interest within a patient, each contour being defined by a plurality of the data points and having a corresponding plane, wherein the plurality of data points are reduced as described above and processed to find the reduced data points that intersect a new plane, and wherein Bspline interpolation is used to interpolate through the points of intersection to generate a new contour in the new plane. This embodiment can operate on a plurality of contours drawn by a user in the S and/or C viewing planes to generate a T contour in a desired T plane. The point reduction operation performed prior to the Bspline interpolation improves the efficiency of the Bspline interpolation operation.
While various advantages and features of several embodiments of the invention have been discussed above, a greater understanding of the invention including a fuller description of its other advantages and features may be attained by referring to the drawings and the detailed description of the preferred embodiment which follow.
The embodiments of the present invention address contours. Contours are planar, closed curves C(x, y, z) which can be realized as sets of nonuniformly sampled points along the userinput stroke, {c_{1}, . . . , c_{M}} (or sets of points generated by an autothresholding and/or autosegmentation program), wherein the individual points are represented by c_{i}=C(x_{i}, y_{i}, z_{i}), and wherein M is the number of points in the contour. Points c_{i }in the T planes (xzplanes) have y constant, S contours (yzplanes) have x constant, and C contours (xyplanes) have z constant.
Contours can also be parameterized by a curve length u where the curve C of length L is represented as C(x, y, z)=C(x(u), y(u), z(u))=C(u) where 0≦u≦L and C(0)=C(L)
When contours exist as discrete points as noted above, it can be useful to represent these points as samples on a continuous curve along which one can interpolate the contour shape at any arbitrary point. Bsplines, which can specify arbitrary curves with great exactness, can provide such a representation for contours. (See Piegl, L. A., and Tiller, W., The Nurbs Book, Springer, New York, 1996, the entire disclosure of which is incorporated herein by reference). The Bspline description of a curve depends on (1) a set of predefined basis functions, (2) a set of geometric control points, and (3) a sequence of real numbers (knots) that specify how the basis functions and control points are composed to describe the curve shape. Given this information, the shape of C(u) can be computed at any u. Alternatively, given points u′ sampled along C(u), one can deduce a set of Bspline control points and corresponding knots that reconstruct the curve to arbitrary accuracy. Thus, Bsplines can be used to interpolate curves or surfaces through geometric points or to approximate regression curves through a set of data points.
Bsplines form piecewise polynomial curves along u, delimited by the knots u_{i},i=0, . . . , m into intervals in which subsets of the basis functions and the control points define C(u). The m+1 knots U={u_{0}, . . . , u_{m}} are a nondecreasing sequence of real numbers such that u_{i}≦u_{i+1}, for all i.
The pth degree Bspline basis function, N_{i,p}(u), defined for the ith knot interval, defines the form of the interpolation. The zeroth order function, N_{i,0}(u), is a step function and higher orders are linear combinations of the lower order functions. The construction of basis functions by recursion is described in the abovereferenced work by Piegl and Tiller. A preferred embodiment of the present invention described herein employs cubic (p=3) Bsplines.
Basis function N_{i,p}(u) is nonzero on the halfopen interval [u_{i}, u_{i+p+1}), and for any interval [u_{i}, u_{i+1}) at most (p+1) of the basis functions, N_{i−p,p}(u), . . . , N_{ix,p}(u), are nonzero. A pth degree, open Bspline curve C(u) with end points u=a,b is defined by
where the P_{i }are the (n+1) control points, the N_{i,p}(u) are the basis functions, and the knot vector U is defined
where a≦u_{p+1}≦u_{p+2}, . . . ≦u_{m−p−1}≦b. This defines an unclosed curve with multiple knots at the end values a=u_{0}, . . . , u_{p};b=u_{m−p}, . . . , u_{m}. For a spline of degree p with m+1 knots, n+1 control points will be required to specify the shape; for all spline geometries p, n, m are related as
m=n+p+1. (3)
Closed curves with coincident start and end points and with C^{2 }continuity (continuous curve with continuous first and second derivatives) throughout are defined with uniform knot vectors of the form U={u_{0}, u_{1}, . . . , u_{m}} with n+1(=m−p) control points defined such that the first p control points P_{0}, P_{1}, . . . , P_{p−1 }are replicated as the last p control points P_{n−p−1}, . . . , P_{m }which for the cubic (p=3) case means that P_{0}=P_{n−2}, P_{1}=P_{n−1}, P_{2}=P_{n}. This means that there are actually n+1−p unique control points, and that the knots that are actually visualizable on a closed curve are the set u_{p}, u_{p+1}, . . . , u_{m−p−1}.
U=(0,1,2,3,4,5,6,7,8,9,10,11)
For fixed p, n, U, the curve shape 300 can be changed by moving one or more of the control points P. The locations of the knots are shown as dots on curve 300, wherein the knots u_{3}u_{7 }uniquely span the curve, wherein knots u_{0}u_{2 }coincide with knots u_{5}u_{7}, and wherein knots u_{8}u_{11 }coincide with knots u_{3}u_{6}. Thus, as with the control points that must be duplicated for cyclic Bspline curves, so too must some of the knots be duplicated.
A useful application of Bsplines is to interpolate a smooth curve through a series of isolated points that represent samples of a curve. Global interpolation can be used to determine a set of control points given all the data in the input curve. (See Chapter 9 of the abovereferenced work by Piegl and Tiller). Suppose one starts with a set of points {Q_{k}}, k=0, . . . , n on the actual curve, and the goal is to interpolate through these points with a pdegree Bspline curve. Assigning a parameter value ū_{k }to each Q_{k }and selecting an appropriate knot vector U={u_{0}, . . . , u_{n}}, one can then set up the (n+1)×(n+1) system of linear equations
where the n+1 control points P_{i }are the unknowns. The system can be rewritten as
Q=AP (5)
where the Q,P are column vectors of the Q_{k }and P_{i}, respectively, and where A is the matrix of basis functions. This (n+1)×(n+1) linear system can be solved for the unknown control points P_{i }
P=A ^{−1}Q (6)
by factoring A by LU decomposition instead of inverting matrix A. (See Press, et al., Numerical Recipes in C, 2^{nd }Edition, Cambridge University Press, 1992; Golub, G. H. and Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, Baltimore, 1996, the entire disclosures of both of which are incorporated herein by reference). A higher quality reconstruction—end points joined with C^{2 }continuity—can be obtained by restricting curves to cubic (p=3) type and by specifying endpoint first derivatives. Defining the endpoint tangent vectors D_{0 }at Q_{0 }and D_{n }at Q_{n}, one constructs a linear system like equation (5) but with two more variables to encode the tangent information resulting in a (n+3)×(n+3) system. The tangents are added to the system with the equations
that can be used to construct a tridiagonal system
that can be solved by Gaussian elimination. (See Chapter 9.2.3 of the abovereferenced work by Piegl and Tiller).
To demonstrate the interpolation of points representing a putative curve, the inventor has sampled points from closed curves with random, but known, shapes, and reconstructed the random curves measuring the accuracy as the mean squared error of the reconstructed curve versus the original.
In the embodiment of
One observation that can be made from
The inventor herein discloses three techniques that can be used to reduce the data points 500 to a plurality of shapesalient points.
According to a first technique of point reduction for step 604, the shapesalient points for each initial input point set are determined as a function of computed curvature values for a contour defined by the points 500 within that initial input point set. The curvature is representative of the speed at which curve C(u) changes direction with respect to increasing u, wherein u represents the distance along curve C(u) beginning from an arbitrary starting point or origin. The curvature of a plane curve is defined as:
where x′=dx/du, x″=d^{2}x/du^{2}, etc. are derivatives computed by finite differences on uniform u− intervals along C(u), and where the x,y values correspond to points which are representative of the input contour. (See DoCarmo, M., Differential Geometry of Curves and Surfaces, Prentice Hall, New York, 1976; Thomas, J. W., Numerical Partial Differential EquationsFinite Difference Methods, Springer, New York, 1995, the entire disclosures of which are incorporated herein by reference).
Preferably, step 604 takes points u* at peak values of κ(u)
u*=arg max_{u}κ(u) (10)
These points u*, which contribute most importantly to the shape of a curve, are saved for reconstruction of the contour through Bspline interpolation. It should be noted that because of the cyclic nature of the data in u (since 0≦u≦L and C(0)=C(L)), when computing the argmax function over intervals u, one can let the intervals span the origin 0 and then reset the computation for intervals placed at L+a to a or −a to L−a. To accomplish the use of uniform intervals u along C(u), one can (1) reconstruct each input contour via Bspline interpolation through all of its raw input points, (2) step along the reconstructed contour in equal size steps that are smaller than the normal spacing among the raw input points to generate the points which are fed to the curvature computation of formula (9), and (3) apply the curvature computations of formulas (9) and (10) to thereby generate a set of reduced points from the original set of raw input points.
It should also be noted that rather than using only maxima, step 604 can also be configured to retain only those points for which the computed curvature value exceeds a threshold value. As such, it can be seen that a variety of conditions can be used for determining how the curvature values will be used to define the shapesalient points.
According to a second technique of point reduction for step 604, the shapesalient points for each initial input point set are determined as a function of computed scalar second derivative a values (i.e., the scalar acceleration) for the motion of a point along C(u), which is defined as
Preferably, step 604 takes points u* at peak values of a(u),
u*=arg max_{u } a(u) (12)
Once again, the derivatives can be computed by finite differences on uniform u− intervals along C(u). Also, as noted above, because of the cyclic nature of the data in u (since 0≦u≦L and C(0)=C(L)), when computing the argmax function over intervals u, one can let the intervals span the origin 0 and then reset the computation for intervals placed at L+a to a or −a to L−a. As with the curvature calculations described above, to accomplish the use of uniform intervals u along C(u), one can (1) reconstruct each input contour via Bspline interpolation through all of its raw input points, (2) step along the reconstructed contour in equal size steps that are smaller than the normal spacing among the raw input points to generate the points which are fed to the scalar second derivative computation of formula (11), and (3) apply the scalar second derivative computation of formulas (11) and (12) to thereby generate a set of reduced points from the original set of raw input points.
It should also be noted that rather than using only maxima, step 604 can also be configured to retain only those points for which the computed scalar second derivative exceeds a threshold value. As such, it can be seen that a variety of conditions can be used for determining how the scalar second derivative values will be used to define the shapesalient points.
According to a third technique of point reduction for step 604, the shapesalient points are determined as a function of the DeBoor equal energy theorem. (See DeBoor, C., A Practical Guide to Splines, Springer, New York, 2001, the entire disclosure of which is incorporated herein by reference). With the DeBoor equal energy theorem, the total curvature of the entire curve is divided into s equal parts, and the sampled points are placed along the curve, at s nonuniform intervals, but in such a way as to divide the total curvature into equal parts.
The DeBoor theorem then measures the curvature as the kth root of absolute value of the kth derivative of the curve,
where D^{k}C(u) denotes the derivative operator. The abovereferenced work by DeBoor proves two instances of a theorem (Theorem II(20), Theorem XII(34)) that optimally places breakpoints (sample points) to interpolate a curve with minimum error. For a closed curve C(u) of length L such that 0≦u<L, one can define a set of arc length values υ_{j}, j=1, . . . , s such that points on C at those values evenly divide the total curvature. The total curvature K is
so that dividing it into s equal parts where the energy of any part is 1/s of the energy of the curve, or
This measure is similar to the ∫(D^{k}C(u))^{2}du “bending energy” curvature measure (see Wahba, G., Spline Models for Observational Data, SIAM (Society for Industrial and Applied Mathematics), Philadelphia, Pa., 1990, the entire disclosure of which is incorporated herein by reference) minimized by spline functions, so it is deemed appropriate to call the DeBoor technique described herein as an “equal energy” theorem or method.
Returning to
Next, step 608 operates to find the points of intersection within each reduced set of reordered points on a desired new plane (e.g., a plane that is nonparallel to the at least one viewing plane for the contours defined by the reduced sets of input points). Preferably, step 608 operates to find the points within each reduced reordered point set that intersect a desired T plane.
After the points of intersection in the new plane (e.g., a T plane) are found, step 610 operates to generate a new contour in this new plane by ordering the points of intersection and interpolating through the points of intersection using Bspline interpolation as described above in Section III.
Thereafter, at step 612, a comparison can be made between the new contour generated at step 610 and a corresponding patient image in the same plane. Such a comparison can be made visually by a user. If the generated contour is deemed a “match” to the image (i.e., a close correspondence between the generated contour and the corresponding anatomy in the displayed image), then the generated contour can be archived for later use (step 614). If the generated contour is not deemed a match to the image, then process flow of
Furthermore, as can be seen in
In the embodiment of
Next, at step 1404, each initial point set is processed to generate a reduced set of input points, as described above in connection with step 604 of
Thereafter, at step 1406, a variational implicit surface is generated from the reduced sets of data points. The variational implicit surface is a solution to the scattered data interpolation problem in which the goal is to determine a smooth function that passes through discrete data points. (See Turk and O'Brien, Shape Transformation Using Variational Implicit Functions, Proceedings of SIGGRAPH 99, Annual Conference Series, pp. 335342, Los Angeles, Calif., August 1999, the entire disclosure of which is incorporated herein by reference). For a set of constraint points {c_{1}, . . . , c_{k}} with a scalar height {h_{1}, . . . , h_{k}} at each position, one can determine a function ƒ(x),x=(x, y, z)^{T }that passes through each c_{i }such that ƒ(c_{i})=h_{i}. A variational solution that minimizes the socalled “bending energy” (see the abovereferenced work by Turk and O'Brien) is the sum
over radial basis functions φ_{j }(described below) weighted by scalar coefficients d_{j}, and where c_{j }are the constraint point locations and P(x) is a degree one polynomial
P(x)=p _{0} +p _{1} x+p _{2} y (17)
that accounts for constant and linear parts of the function ƒ(x). The radial basis functions for the 3D constraints appropriate for this problem are
φ(x)=x ^{3}. (18)
Solving for the constraints h_{i }in terms of the known positions
gives a linear system that for 3D constraints c=(c_{i} ^{x}, c_{i} ^{y}, c_{i} ^{z}) is
This system is symmetric and positive semidefinite, so there will always be a unique solution for the d_{j }and the p_{j}. The solution can be obtained using LU decomposition. (See the abovereferenced works by Press et al. and Golub and Van Loan). In a preferred embodiment, the implementation of LU decomposition can be the LAPACK implementation that is known in the art. (See Anderson et al., LAPACK User's Guide, Third Edition, SIAM—Society for Industrial and Applied Mathematics, Philadelphia, 1999, the entire disclosure of which is incorporated herein by reference).
A further feature of the variational implicit surface computation as described in the abovereferenced work by Turk and O'Brien is the use of additional constraint points, located off the boundary along normals connecting with the onboundary constraints, to more accurately and reliably interpolate the surface through the onboundary constraints. In a preferred embodiment, the onboundary constraints' h_{j }values can be set to 0.0 and the offboundary values can be set to 1.0. However, as should be understood, other values can be used in the practice of this embodiment of the invention.
Performance of this solution depends partly on the form of the radial basis function φ(x) one uses, and on the size of the system parameter k (number of all constraint points). The performance of the LU solution of equation (20) can be done using different choices of φ. (See Dinh, et al., Reconstructing surfaces by volumetric regularization using radial basis functions, IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, pp. 13581371, 2002, the entire disclosure of which is incorporated herein by reference). The function x^{3} is monotonic increasing, meaning that the matrix in (20) has large offdiagonal values for all constraint point pairs c_{i}, c_{j}, i≠j. To make the linear system perform more robustly, the abovereferenced work by Dinh describes a modification of the system to make it more diagonally dominant by adding to the diagonal elements a set of scalar values λ_{i}
A preferred embodiment uses values λ_{Boundary}=0.001 and λ_{OffBoundary}=1.0. However, it should be understood that other values could be used.
After solving for the d_{j }and the p_{j }in Equation (20), the implicit function in (16) can be evaluated to determine that set of points {x_{i}} for which ƒ(x_{i})=0. (The zeroth level of ƒ(x) is that on which the boundary points lie). The method of Bloomenthal (see Bloomenthal, J., An Implicit Surface Polygonizer, Graphics Gems IV, P. Heckbert, Ed., Academic Press, New York, 1994, the entire disclosure of which is incorporated herein by reference) can be used to track around the function and determine the locations of mesh nodes from which a 3D surface may be constructed. A closed surface constructed in this way can be termed a variational implicit surface. (See the abovereferenced work by Turk and O′Brien).
At step 1408, that mesh can then be clipped by planes parallel to the xzplane at the appropriate yvalue(s) to produce the desired T contour(s) for display to the user. The mesh representation and clipping functionality can be performed using the VTK software system available from Kitware, Inc. of Clifton Park, N.Y. (See Schroeder et al., The Visualization Toolkit, 4^{th } Ed., Kitware, 2006, the entire disclosure of which is incorporated herein by reference).
Thereafter, as with steps 612 and 614 of
As indicated, the main performance limitation for computing a variational implicit surface is the total number of constraints, and for k greater than a few thousand, the variational implicit surface computation takes too much time to be useful for realtime applications. However, the inventor herein believes that by reducing the number of constraint points used for computing the variational implicit surface via any of the compression operations described in connection with steps 1404 and 604 for contour representations, the computation of variational implicit surfaces will become practical for 3D medical contouring. Furthermore, a fortunate property of the variational implicit surface is its ability to forgive small mismatches in orthogonal contours that are required to intersect (because they are curves on the same surface) but do not because the user was unable to draw them carefully enough. For example, when the sampling interval in the Bloomenthal algorithm is set to the interT plane distance, the resulting surfaces are sampled at too coarse a level to reveal the small wrinkles in the actual surface, and the resulting T contours are not affected by the missed T/S/C intersections.
In
In
As shown by
It should also be noted that it may sometimes be the case wherein an initial set of input points corresponding to a contour contains only a small number of points, long gaps in the sequence of input points, and/or two or more points having the same coordinates (x,y). For example, both a small number of points and long gaps between points would likely result when a user defines a contour by only picking points at the vertices of a polygon that approximates the contour. Duplicate points can result when the user picks points along a contour because a graphics subsystem will sometimes interpret a single mouse button push as multiple events. In such instances, the process flow of
It should also be noted that the Bspline interpolation and variational implicit surface generation can be combined in a single process flow as different modes of operation, as shown in
If the Bspline interpolation mode is used, then steps 2106 and 2108 can be performed, wherein these steps correspond to steps 606 and 608 from
If the variational implicit surface mode is used, then steps 1404, 1406, and 1408 can be followed as described in connection with
While the present invention has been described above in relation to its preferred embodiments, various modifications may be made thereto that still fall within the invention's scope. Such modifications to the invention will be recognizable upon review of the teachings herein. Accordingly, the full scope of the present invention is to be defined solely by the appended claims and their legal equivalents.
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US8098909B2 (en)  20070831  20120117  Computerized Medical Systems, Inc.  Method and apparatus for efficient threedimensional contouring of medical images 
US7978191B2 (en) *  20070924  20110712  Dolphin Imaging Systems, Llc  System and method for locating anatomies of interest in a 3D volume 
US8265356B2 (en) *  20080130  20120911  Computerized Medical Systems, Inc.  Method and apparatus for efficient automated recontouring of fourdimensional medical imagery using surface displacement fields 
US8994724B2 (en) *  20101217  20150331  IntegrityWare, Inc.  Methods and systems for generating continuous surfaces from polygonal data 
US8867806B2 (en)  20110801  20141021  Impac Medical Systems, Inc.  Method and apparatus for correction of errors in surfaces 
US9142042B2 (en) *  20110913  20150922  University Of Utah Research Foundation  Methods and systems to produce continuous trajectories from discrete anatomical shapes 
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USD752222S1 (en)  20130514  20160322  Laboratoires Bodycad Inc.  Femoral prosthesis 
USD702349S1 (en)  20130514  20140408  Laboratories Bodycad Inc.  Tibial prosthesis 
US9697600B2 (en)  20130726  20170704  Brainlab Ag  Multimodal segmentatin of image data 
US9355447B2 (en) *  20130821  20160531  Wisconsin Alumni Research Foundation  System and method for gradient assisted nonconnected automatic region (GANAR) analysis 
GB201413721D0 (en) *  20140801  20140917  Mirada Medical Ltd  Method and apparatus for delineating an object within a volumetric medical image 
USD808524S1 (en)  20161129  20180123  Laboratoires Bodycad Inc.  Femoral implant 
Citations (33)
Publication number  Priority date  Publication date  Assignee  Title 

US5859891A (en) *  19970307  19990112  Hibbard; Lyn  Autosegmentation/autocontouring system and method for use with threedimensional radiation therapy treatment planning 
US6075538A (en) *  19960725  20000613  Institute Of High Performance Computing  Time and space efficient data structure and method and apparatus for using the same for surface rendering 
US6112109A (en) *  19930910  20000829  The University Of Queensland  Constructive modelling of articles 
US6142019A (en)  19980629  20001107  General Electric Co.  Method of determining surface acoustic wave paths 
US6259943B1 (en)  19950216  20010710  Sherwood Services Ag  Frameless to framebased registration system 
US6262739B1 (en)  19961016  20010717  RealTime Geometry Corporation  System and method for computer modeling of 3D objects or surfaces by mesh constructions having optimal quality characteristics and dynamic resolution capabilities 
US6343936B1 (en)  19960916  20020205  The Research Foundation Of State University Of New York  System and method for performing a threedimensional virtual examination, navigation and visualization 
US6606091B2 (en)  20000207  20030812  Siemens Corporate Research, Inc.  System for interactive 3D object extraction from slicebased medical images 
US6683933B2 (en)  20010502  20040127  Terarecon, Inc.  Threedimensional image display device in network 
US20050168461A1 (en)  20001030  20050804  Magic Earth, Inc.  System and method for analyzing and imaging threedimensional volume data sets 
US6947584B1 (en)  19980825  20050920  General Electric Company  Volume imaging system 
US20050231530A1 (en)  20040415  20051020  ChengChung Liang  Interactive 3D data editing via 2D graphical drawing tools 
US20050276455A1 (en)  20040601  20051215  Marta Fidrich  Systems and methods for segmenting an organ in a plurality of images 
US7010164B2 (en)  20010309  20060307  Koninklijke Philips Electronics, N.V.  Image segmentation 
US20060147114A1 (en)  20030612  20060706  Kaus Michael R  Image segmentation in timeseries images 
US20060149511A1 (en)  20021212  20060706  Michael Kaus  Method of segmenting a threedimensional data set allowing user corrections 
US20060159341A1 (en)  20030613  20060720  Vladimir Pekar  3D image segmentation 
US20060159322A1 (en)  20040909  20060720  Daniel Rinck  Method for segmentation of anatomical structures from 4D image data records 
US20060177133A1 (en)  20041127  20060810  Bracco Imaging, S.P.A.  Systems and methods for segmentation of volumetric objects by contour definition using a 2D interface integrated within a 3D virtual environment ("integrated contour editor") 
US20060204040A1 (en)  20050307  20060914  Freeman William T  Occluding contour detection and storage for digital photography 
US7110583B2 (en) *  20010131  20060919  Matsushita Electric Industrial, Co., Ltd.  Ultrasonic diagnostic device and image processing device 
US20060256114A1 (en)  20050331  20061116  Sony Corporation  Image processing apparatus and image processing method 
US20070014462A1 (en)  20050713  20070118  Mikael Rousson  Constrained surface evolutions for prostate and bladder segmentation in CT images 
US7167172B2 (en)  20010309  20070123  Koninklijke Philips Electronics N.V.  Method of segmenting a threedimensional structure contained in an object, notably for medical image analysis 
US20070041639A1 (en)  20030218  20070222  Jens Von Berg  Image segmentation by assigning classes to adaptive mesh primitives 
US20070092115A1 (en)  20051026  20070426  Usher David B  Method and system for detecting biometric liveness 
US20070167699A1 (en)  20051220  20070719  Fabienne Lathuiliere  Methods and systems for segmentation and surface matching 
US7333644B2 (en)  20030311  20080219  Siemens Medical Solutions Usa, Inc.  Systems and methods for providing automatic 3D lesion segmentation and measurements 
US7428334B2 (en)  20040827  20080923  General Electric Company  Methods and systems for 3D segmentation of ultrasound images 
US20090016612A1 (en)  20050928  20090115  Koninklijke Philips Electronics, N.V.  Method of reference contour propagation and optimization 
US20090190809A1 (en)  20080130  20090730  Xiao Han  Method and Apparatus for Efficient Automated ReContouring of FourDimensional Medical Imagery Using Surface Displacement Fields 
US7620224B2 (en) *  20040811  20091117  Ziosoft, Inc.  Image display method and image display program 
US8098909B2 (en)  20070831  20120117  Computerized Medical Systems, Inc.  Method and apparatus for efficient threedimensional contouring of medical images 
Patent Citations (34)
Publication number  Priority date  Publication date  Assignee  Title 

US6112109A (en) *  19930910  20000829  The University Of Queensland  Constructive modelling of articles 
US6259943B1 (en)  19950216  20010710  Sherwood Services Ag  Frameless to framebased registration system 
US6075538A (en) *  19960725  20000613  Institute Of High Performance Computing  Time and space efficient data structure and method and apparatus for using the same for surface rendering 
US6343936B1 (en)  19960916  20020205  The Research Foundation Of State University Of New York  System and method for performing a threedimensional virtual examination, navigation and visualization 
US6262739B1 (en)  19961016  20010717  RealTime Geometry Corporation  System and method for computer modeling of 3D objects or surfaces by mesh constructions having optimal quality characteristics and dynamic resolution capabilities 
US5859891A (en) *  19970307  19990112  Hibbard; Lyn  Autosegmentation/autocontouring system and method for use with threedimensional radiation therapy treatment planning 
US6142019A (en)  19980629  20001107  General Electric Co.  Method of determining surface acoustic wave paths 
US6947584B1 (en)  19980825  20050920  General Electric Company  Volume imaging system 
US6606091B2 (en)  20000207  20030812  Siemens Corporate Research, Inc.  System for interactive 3D object extraction from slicebased medical images 
US20050168461A1 (en)  20001030  20050804  Magic Earth, Inc.  System and method for analyzing and imaging threedimensional volume data sets 
US7110583B2 (en) *  20010131  20060919  Matsushita Electric Industrial, Co., Ltd.  Ultrasonic diagnostic device and image processing device 
US7167172B2 (en)  20010309  20070123  Koninklijke Philips Electronics N.V.  Method of segmenting a threedimensional structure contained in an object, notably for medical image analysis 
US7010164B2 (en)  20010309  20060307  Koninklijke Philips Electronics, N.V.  Image segmentation 
US6683933B2 (en)  20010502  20040127  Terarecon, Inc.  Threedimensional image display device in network 
US20060149511A1 (en)  20021212  20060706  Michael Kaus  Method of segmenting a threedimensional data set allowing user corrections 
US20070041639A1 (en)  20030218  20070222  Jens Von Berg  Image segmentation by assigning classes to adaptive mesh primitives 
US7333644B2 (en)  20030311  20080219  Siemens Medical Solutions Usa, Inc.  Systems and methods for providing automatic 3D lesion segmentation and measurements 
US20060147114A1 (en)  20030612  20060706  Kaus Michael R  Image segmentation in timeseries images 
US20060159341A1 (en)  20030613  20060720  Vladimir Pekar  3D image segmentation 
US20050231530A1 (en)  20040415  20051020  ChengChung Liang  Interactive 3D data editing via 2D graphical drawing tools 
US20050276455A1 (en)  20040601  20051215  Marta Fidrich  Systems and methods for segmenting an organ in a plurality of images 
US7620224B2 (en) *  20040811  20091117  Ziosoft, Inc.  Image display method and image display program 
US7428334B2 (en)  20040827  20080923  General Electric Company  Methods and systems for 3D segmentation of ultrasound images 
US20060159322A1 (en)  20040909  20060720  Daniel Rinck  Method for segmentation of anatomical structures from 4D image data records 
US20060177133A1 (en)  20041127  20060810  Bracco Imaging, S.P.A.  Systems and methods for segmentation of volumetric objects by contour definition using a 2D interface integrated within a 3D virtual environment ("integrated contour editor") 
US20060204040A1 (en)  20050307  20060914  Freeman William T  Occluding contour detection and storage for digital photography 
US20060256114A1 (en)  20050331  20061116  Sony Corporation  Image processing apparatus and image processing method 
US20070014462A1 (en)  20050713  20070118  Mikael Rousson  Constrained surface evolutions for prostate and bladder segmentation in CT images 
US20090016612A1 (en)  20050928  20090115  Koninklijke Philips Electronics, N.V.  Method of reference contour propagation and optimization 
US20070092115A1 (en)  20051026  20070426  Usher David B  Method and system for detecting biometric liveness 
US20070167699A1 (en)  20051220  20070719  Fabienne Lathuiliere  Methods and systems for segmentation and surface matching 
US8098909B2 (en)  20070831  20120117  Computerized Medical Systems, Inc.  Method and apparatus for efficient threedimensional contouring of medical images 
US20120057769A1 (en)  20070831  20120308  Hibbard Lyndon S  Method and Apparatus for Efficient ThreeDimensional Contouring of Medical Images 
US20090190809A1 (en)  20080130  20090730  Xiao Han  Method and Apparatus for Efficient Automated ReContouring of FourDimensional Medical Imagery Using Surface Displacement Fields 
NonPatent Citations (102)
Title 

Adelson et al., "Pyramid Methods in Image Processing", RCA Engineer, Nov./Dec. 1984, pp. 3341, vol. 296. 
Anderson et al., "LAPACK User's Guide", Third Edition, SIAMSociety for Industrial and Applied Mathematics, 1999, Philadelphia. 
Anderson et al., "LAPACK User's Guide", Third Edition, SIAM—Society for Industrial and Applied Mathematics, 1999, Philadelphia. 
Barrett et al., "Interactive LiveWire Boundary Extraction", Medical Image Analysis, 1, 331341, 1997. 
Bertalmio et al., "Morphing Active Countours", IEEE Trans. Patt. Anal. Machine Intell., 2000, pp. 733737, vol. 22. 
Bloomenthal, "An Implicit Surface Polygonizer", Graphics Gems IV, P Heckbert, Ed., Academic Press, New York, 1994. 
Bookstein, "Principal Warps: ThinPlate Splines and the Decomposition of Deformations", IEEE Transactions on Pattern Analysis and Machine Intelligence, Jun. 1989, pp. 567585, vol. 11, No. 6. 
Botsch et al., "On Linear Variational Surface Deformation Methods", IEEE Transactions on Visualization and Computer Graphics, 2008, pp. 213230, vol. 14, No. 1. 
Burnett et al., "A DeformableModel Approach to SemiAutomatic Segmentation of CT Images Demonstrated by Application to the Spinal Canal", Med. Phys., Feb. 2004, pp. 251263, vol. 31 (2). 
Carr et al., "Reconstruction and Representation of 3D Objects with Radial Basis Functions", Proceedings of SIGGRAPH 01, pp. 6776, 2001. 
Carr et al., "Surface Interpolation with Radial Basis Functions for Medical Imaging", IEEE Transactions on Medical Imaging, 16, 96107, 1997. 
Cover et al., "Elements of Information Theory", Chapter 2, 1991, Wiley, New York, 33 pages. 
Cover et al., "Elements of Information Theory", Chapter 8, 1991, Wiley, New York, 17 pages. 
Cruz et al., "A sketch on SketchBased Interfaces and Modeling", Graphics, Patterns and Images Tutorials, 23rd SIBGRAPI Conference, 2010, pp. 2233. 
Davis et al., "Automatic Segmentation of IntraTreatment CT Images for Adaptive Radiation Therapy of the Prostate", presented at 8th Int. Conf. MICCAI 2005, Palm Springs, CA, pp. 442450. 
De Berg et al., "Computational Geometry: Algorithms and Applications", 1997, Chapter 5, SpringerVerlag, New York. 
DeBoor, "A Practical Guide to Splines", Springer, New York, 2001. 
Dice's coeffieient, Wikipedia, 1945. 
Digital Imaging and Communications in Medicine (DICOM), http://medical.nema.org/. 
Dinh et al., "Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions", IEEE Trans. Patt. Anal. Mach. Intell., 24, 13581371, 2002. 
Dinh et al., "Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions", IEEE Transactions on Pattern Analysis and Machine Intelligence, Oct. 2002, pp. 13581371, vol. 24, No. 10. 
Dinh et al., "Texture Transfer During Shape Transformation", ACM Transactions on Graphics, 24, 289310, 2005. 
DoCarmo, "Differential Geometry of Curves and Surfaces", Prentice Hall, New Jersey, 1976. 
Duchon, "Splines Minimizing RotationInvariant SBMINORMS in Soboley Spaces", 1977, Universite Scientifique et Medicale Laboratoire de Mathematiques Appliques, Grenoble France. 
Falcao et al., "An UltraFast UserSteered Image Segmentation Paradigm: Live Wire on the Fly", IEEE Transactions on Medical Imaging, 19, 5562, 2000. 
Freedman et al., "Active Contours for Tracking Distributions", IEEE Trans. Imag. Proc., Apr. 2004, pp. 518526, vol. 13 (4). 
Gao et al., "A Deformable Image Registration Method to Handle Distended Rectums in Prostate Cancer Radiotherapy", Med. Phys., Sep. 2006, pp. 33043312, vol. 33 (9). 
Gelas et al., "Variatonal Implicit Surface Meshing", Computers and Graphics, 2009, pp. 312320, vol. 33. 
Gering et al., "An Integrated Visualization System for Surgical Planning and Guidance Using Image Fusion and an Open MR", Journal of Magnetic Resonance Imaging, 13, 967975, 2001. 
Gering et al., "An Integrated Visualization System for Surgical Planning and Guidance using Image Fusion and Interventional Imaging", Int Conf Med Image Comput Assist Interv, 1999, pp. 809819, vol. 2. 
Gering, "A System for Surgical Planning and Guidance Using Image Fusion and Interventional MR", MS Thesis, MIT, 1999. 
Girosi et al., "Priors, Stabilizers and Basis Functions: from regularization to radial, tensor and additive splines", Massachusetts Institute of Technology Artificial Intelligence Laboratory, Jun. 1993, 28 pages. 
Golub et al., "Matrix Computations", Third Edition, The Johns Hopkins University Press, Baltimore, 1996. 
Han et al., "A Morphing Active Surface Model for Automatic ReContouring in 4D Radiotherapy", Proc. of SPIE, 2007, vol. 6512, 9 pages. 
Ho et al., "SNAP: A Software Package for UserGuided Geodesic Snake Segmentation", Technical Report, UNC Chapel Hill, Apr. 2003. 
Huang et al., "SemiAutomated CT Segmentation Using Optic Flow and Fourier Interpolation Techniques", Computer Methods and Programs in Biomedicine, 84, 124134, 2006. 
Ibanez et al., "The ITK Software Guide" Second Edition, 2005. 
Igarashi et al., "Smooth Meshes for Sketchbased Freeform Modeling" In ACM Symposium on Interactive 3D Graphics, (ACM I3D'03), pp. 139142, 2003. 
Igarashi et al., "Teddy: A Sketching Interface for 3D Freeform Design", Proceedings of SIGGRAPH 1999, 409416. 
Ijiri et al., "Seamless Integration of Initial Sketching and Subsequent Detail Editing in Flower Modeling", Eurographics 2006, 25, 617624, 2006. 
International Search Report and Written Opinion for PCT/US2012/048938 dated Oct. 16, 2012. 
Jackowski et al., "A ComputerAided Design System for Refinement of Segmentation Errors", MICCAI 2005, LNCS 3750, pp. 717724. 
Jain et al., "Deformable Template Models: A Review", Signal Proc., 1998, pp. 109129, vol. 71. 
Jain, "Fundamentals of Digital Image Processing", PrenticeHall, New Jersey, 1989. 
JehanBesson et al., "Shape Gradients for Histogram Segmentation Using Active Contours", 2003, presented at the 9th IEEE Int. Conf. Comput. Vision, Nice, France, 8 pages. 
Kalbe et al., "HighQuality Rendering of Varying Isosurfaces with Cubic Trivariate C1continuous Splines", ISVC 1, LNCS 5875, 2009, pp. 596607. 
Kalet et al., "The Use of Medical Images in Planning and Delivery of Radiation Therapy", J. Am. Med. Inf. Assoc., Sep./Oct. 1997, pp. 327339, vol. 4 (5). 
Karpenko et al., "FreeForm Sketching with Variational Implicit Surfaces", Computer Graphics Forum, 21, 585594, 2002. 
Karpenko et al., "SmoothSketch: 3D FreeForm Shapes From Complex Sketches", Proceedings of SIGGRAPH 06, pp. 589598. 
Kaus et al., "Automated 3D PDM Construction From Segmented Images Using Deformable Models", IEEE Transactions on Medical Imaging, Aug. 2003, pp. 10051013, vol. 22, No. 8. 
Kho et al., "Sketching Mesh Deformations", ACM Symposium on Interactive 3D Graphics and Games, 2005, 8 pages. 
Knoll et al., "Fast and Robust Ray Tracing of General Implicits on the GPU", Scientific Computing and Imaging Institute, University of Utah, Technical Report No. UUSCI2007014, 2007, 8 pages. 
Leventon et al., "Statistical Shape Influence in Geodesic Active Contours", IEEE Conference on Computer Vision and Pattern Recognition, 2000, pp. 13161323. 
Leymarie et al., "Tracking Deformable Objects in the Plane Using an Active Contour Model", IEEE Trans. Patt. Anal. Machine Intell., Jun. 1993, pp. 617634, vol. 15 (6). 
Lipson et al., "Conceptual Design and Analysis by Sketching", Journal of AI in Design and Manufacturing, 14, 391401, 2000. 
Lorenson et al., "Marching Cubes: A High Resolution 3D Surface Construction Algorithm", Computer Graphics, Jul. 1987, pp. 163169, vol. 21 (4). 
Lu et al., "Automatic ReContouring in 4D Radiotherapy", Phys. Med. Biol., 2006, pp. 10771099, vol. 51. 
Lu et al., "Fast FreeForm Deformable Registration Via Calculus of Variations", Phys. Med. Biol., 2004, pp. 30673087, vol. 49. 
Marker et al., "ContourBased Surface Reconstruction Using Implicit Curve Fitting, and Distance Field Filtering and Interpolation", The Eurographics Association, 2006, 9 pages. 
Nealen et al., "A SketchBased Interface for DetailPreserving Mesh Editing", Proceedings of ACM SIGGRAPH 2005, 6 pages, vol. 24, No. 3. 
Notice of Allowance for U.S. Appl. No. 12/022,929 dated May 8, 2012. 
Office Action for U.S. Appl. No. 13/295,525 dated Nov. 28, 2012. 
Osher et al., "Level Set Methods and Dynamic Implicit Surfaces", Chapters 1113, 2003, SpringerVerlag, New York, NY. 
Paragios et al., "Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects", IEEE Trans. Patt. Anal. Machine Intell., Mar. 2000, pp. 266280, vol. 22 (3). 
Pekar et al., "Automated ModelBased Organ Delineation for Radiotherapy Planning in Prostate Region", Int. J. Radiation Oncology Biol. Phys., 2004, pp. 973980, vol. 60 (3 ). 
Pentland et al., "ClosedForm Solutions for Physically Based Shape Modeling and Recognition", IEEE Trans. Patt. Anal. Machine Intell., Jul. 1991, pp. 715729, vol. 13 (7). 
Piegl et al., "The NURBS Book", Second Edition, Springer, New York, 1997. 
Pieper et al., "The NAMIC Kit: ITK, VTK, Pipelines, Grids and 3D Slicer as An Open Platform for the Medical Image Computing Community", Proceedings of the 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro 2006, pp. 698701, vol. 1. 
Pohl et al., "A Bayesian model for joint segmentation and registration", NeuroImage, 2006, pp. 228239, vol. 31. 
Press et al., "Numerical Recipes in C", Second Edition, Cambridge University Press, 1992. 
Rogelj et al., "Symmetric Image Registration", Med. Imag. Anal., 2006, pp. 484493, vol. 10. 
Sapiro, "Geometric Partial Differential Equations and Image Analysis", Chapter 8, 2001, Cambridge University Press. 
Sarrut et al., "Simulation of FourDimensional CT Images from Deformable Registration Between Inhale and Exhale BreathHold CT Scans", Med. Phys., Mar. 2006, pp. 605617, vol. 33 (3). 
Schmidt et al., ShapeShop: SketchBased Solid Modeling with Blob Trees, EUROGRAPHICS Workshop on SketchBased Interfaces and Modeling, 2005. 
Schroeder et al., "The Visualization Toolkit", 2nd edition, Chapter 5, 1998, PrenticeHall, Inc. 
Schroeder et al., "The Visualization Toolkit", 2nd Edition, Kitware, 2006, Ch. 5 & 13, 65 pp. 
Sethian, "Level Set Methods and Fast Marching Methods", 2nd ed., 1999, Cambridge University Press, Chapters 1, 2 & 6, 39 pages. 
Singh et al., "RealTime RayTracing of Implicit Surfaces on the GPU", IEEE Transactions on Visualization and Computer Graphics, 2009, pp. 261272, vol. 99. 
Stefanescu, "Parallel Nonlinear Registration of Medical Images With a Priori Information on Anatomy and Pathology", PhD Thesis. SophiaAntipolis: University of Nice, 2005, 140 pages. 
Strang, "Introduction to Applied Mathematics", 1986, Wellesley, MA: WellesleyCambridge Press, pp. 242262. 
Thirion, "Image Matching as a Diffusion Process: An Analog with Maxwell's Demons", Med. Imag. Anal., 1998, pp. 243260, vol. 2 (3). 
Thomas, "Numerical Partial Differential Equations: Finite Difference Methods", Springer, New York, 1995. 
Tikhonov et al., "Solutions of IIIPosed Problems", IntroductionChapter 2, 1977, John Wiley & Sons. 
Tikhonov et al., "Solutions of IIIPosed Problems", Introduction—Chapter 2, 1977, John Wiley & Sons. 
Tsai et al, "A ShapeBased Approach to the Segmentation of Medical Imagery Using Level Sets", IEEE Transactions on Medical Imaging, Feb. 2003, pp. 137154, vol. 22, No. 2. 
Tsai et al., "An EM algorithm for shape classification based on level sets", Medical Image Analysis, 2005, pp. 491502, vol. 9. 
Turk et al., "Shape Transformation Using Variational Implicit Functions", Proceedings of SIGGRAPH 99, Annual Conference Series, (Los Angeles, California), pp. 335342, Aug. 1999. 
Vemuri et al., "Joint Image Registration and Segmentation", Geometric Level Set Methods in Imaging, Vision, and Graphics, S. Osher and N. Paragios, Editors, 2003, SpringerVerlag, New York, pp. 251269. 
Wahba, "Spline Models for Observational Data", SIAM (Society for Industrial and Applied Mathematics), Philadelphia, PA, 1990. 
Wang et al., "Validation of an Accelerated 'Demons' Algorithm for Deformable Image Registration in Radiation Therapy", Phys. Med. Biol., 2005, pp. 28872905, vol. 50. 
Wang et al., "Validation of an Accelerated ‘Demons’ Algorithm for Deformable Image Registration in Radiation Therapy", Phys. Med. Biol., 2005, pp. 28872905, vol. 50. 
Wolf et al., "ROPES: a Semiautomated Segmentation Method for Accelerated Analysis of ThreeDimensional Echocardiographic Data", IEEE Transactions on Medical Imaging, 21, 10911104, 2002. 
Xing et al., "Overview of ImageGuided Radiation Therapy", Med. Dosimetry, 2006, pp. 91.112, vol. 31 (2). 
Xing et al., "Overview of ImageGuided Radiation Therapy", Med. Dosimetry, 2006, pp. 91•112, vol. 31 (2). 
Xu et al., "Image Segmentation Using Deformable Models", Handbook of Medical Imaging, vol. 2, M. Sonka and J.M. Fitzpatrick, Editors, 2000, SPIE Press, Chapter 3. 
Yezzi et al., "A Variational Framework for Integrating Segmentation and Registration Through Active Contours", Med. Imag. Anal., 2003, pp. 171185, vol. 7. 
Yoo, "Anatomic Modeling from Unstructured Samples Using Variational Implicit Surfaces", Proceedings of Medicine Meets Virtual Reality 2001, 594600. 
Young et al., "RegistrationBased Morphing of Active Contours for Segmentation of CT Scans", Mathematical Biosciences and Engineering, Jan. 2005, pp. 7996, vol. 2 (1). 
Yushkevich et al., "UserGuided 3D Active Contour Segmentation of Anatomical Structures: Significantly Improved Efficiency and Reliability", NeuroImage 31, 11161128, 2006. 
Zagrodsky et al., "RegistrationAssisted Segmentation of RealTime 3D Echocardiographic Data Using Deformable Models", IEEE Trans. Med. Imag., Sep. 2005, pp. 10891099, vol. 24 (9). 
Zeleznik et al., "SKETCH: An Interface for Sketching 3D Scenes", Proceedings of SIGGRAPH 96, 163170, 1996. 
Zhong et al., "Object Tracking Using Deformable Templates", IEEE Trans. Patt. Anal. Machine Intell., May 2000, pp. 544549, vol. 22 (5). 
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